2017/10/11 by Xiao, Yi-Bin, Van Tuyen, Nguyen, Wen, Ching-Feng +1
#49J52 #49J53 #49K30 #90C29 #90C46 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1710.03989
In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some second-order constraint qualifications of Zangwill type, Abadie type and Mangasarian~--~Fromovitz type as well as a regularity condition of Abadie type are proposed in a nonsmooth setting. The connections between these proposed conditions are established. They are applied to develop second-order Karush--Kuhn--Tucker necessary optimality conditions for local (weak, Geoffrion properly) efficient solutions to the considered problem. Examples are also given to illustrate the obtained results.